"""simple docstring"""


from __future__ import annotations

from collections.abc import Callable

a				=list[list[float | int]]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Matrix:




						'''simple docstring'''



						lowerCamelCase__   =len(__lowerCAmelCase							)
						lowerCamelCase__   =[[0 for _ in range(size + 1							)] for _ in range(__lowerCAmelCase							)]
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42

						for row in range(__lowerCAmelCase							):
												for col in range(__lowerCAmelCase							):
																		lowerCamelCase__   =matrix[row][col]

												lowerCamelCase__   =vector[row][0]

						lowerCamelCase__   =0
						lowerCamelCase__   =0
						while row < size and col < size:
												# pivoting
												lowerCamelCase__   =max((abs(augmented[rowa][col]							), rowa) for rowa in range(__lowerCAmelCase  ,       __lowerCAmelCase							)							)[
												    1
												]
												if augmented[pivot_row][col] == 0:
																		col += 1
																		continue
												else:
																		lowerCamelCase__   , lowerCamelCase__   =augmented[pivot_row], augmented[row]

												for rowa in range(row + 1  ,       __lowerCAmelCase							):
																		lowerCamelCase__   =augmented[rowa][col] / augmented[row][col]
																		lowerCamelCase__   =0
																		for cola in range(col + 1  ,       size + 1							):
																								augmented[rowa][cola] -= augmented[row][cola] * ratio

												row += 1
												col += 1

						# back substitution
						for col in range(1  ,       __lowerCAmelCase							):
												for row in range(__lowerCAmelCase							):
																		lowerCamelCase__   =augmented[row][col] / augmented[col][col]
																		for cola in range(__lowerCAmelCase  ,       size + 1							):
																								augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
						return [
						    [round(augmented[row][size] / augmented[row][row]  ,       10							)] for row in range(__lowerCAmelCase							)
						]





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Callable[[int], int]:




						'''simple docstring'''



						lowerCamelCase__   =len(__lowerCAmelCase							)
						lowerCamelCase__   =[[0 for _ in range(__lowerCAmelCase							)] for _ in range(__lowerCAmelCase							)]
						lowerCamelCase__   =[[0] for _ in range(__lowerCAmelCase							)]
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42
						lowerCamelCase__   =42

						for x_val, y_val in enumerate(__lowerCAmelCase							):
												for col in range(__lowerCAmelCase							):
																		lowerCamelCase__   =(x_val + 1) ** (size - col - 1)
												lowerCamelCase__   =y_val

						lowerCamelCase__   =solve(__lowerCAmelCase  ,       __lowerCAmelCase							)

						def interpolated_func(__lowerCAmelCase							) -> int:
												return sum(
												    round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
												    for x_val in range(__lowerCAmelCase							)							)

						return interpolated_func





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						return (
						    1
						    - variable
						    + variable**2
						    - variable**3
						    + variable**4
						    - variable**5
						    + variable**6
						    - variable**7
						    + variable**8
						    - variable**9
						    + variable**10
						)





def      lowerCamelCase_					(   __lowerCAmelCase = question_function  ,       __lowerCAmelCase = 10							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[func(__lowerCAmelCase							) for x_val in range(1  ,       order + 1							)]

						lowerCamelCase__   =[
						    interpolate(data_points[:max_coeff]							) for max_coeff in range(1  ,       order + 1							)
						]

						lowerCamelCase__   =0
						lowerCamelCase__   =42
						lowerCamelCase__   =42

						for poly in polynomials:
												lowerCamelCase__   =1
												while func(__lowerCAmelCase							) == poly(__lowerCAmelCase							):
																		x_val += 1

												ret += poly(__lowerCAmelCase							)

						return ret


if __name__ == "__main__":
	print(F'''{solution() = }''')



"""simple docstring"""


from .imports import is_rich_available


if is_rich_available():
	from rich.traceback import install

	install(show_locals=False)

else:
	raise ModuleNotFoundError('To use the rich extension, install rich with `pip install rich`')


